Heat - The Solid Earth - page 307

Using the values T perhaps 5773 K (5500 ◦ C), estimated from high-pressure
melting

experiments on iron compounds (see Fig. 7.16(b)); α perhaps

10 − 5 ◦ C − 1 ; g , 6ms − 2 ; and c P 10 2 Jkg − 1 ◦ C − 1

∼ 7 × gives an adiabatic gra-

10 − 4 ◦ Cm − 1 (0.5 ◦ Ckm − 1 ). However, because estimates of the ratio dient of 5 ×

α/ c P in the core decrease with depth, the adiabatic gradient in the outer core

decreases with depth from perhaps 0.8 to 0.2 ◦ Ckm − 1 . These estimates are just
that, being reliable perhaps to within 0.3 ◦ Ckm − 1 ; such is the uncertainty in

±

physical properties of the outer core.

7.8 Metamorphism: geotherms in the continental crust
7.8.1 Introduction
Metamorphism is yet another process that is controlled by the transfer and gen-
eration of heat, and understanding of the thermal constraints on metamorphism
is important in attempts to deduce past tectonic and thermal settings from the
metamorphic evidence available to geologists today. Thus, in this section, con-
sidering heat to be transferred by conduction, we study the thermal evolution of
some two-dimensional models of the crust.
Two-dimensional thermal models are conceptually easier to understand than
one-dimensional models, but, except for a few limited cases, simple analytical
solutions to the differential equations are not possible. For the examples shown
here, the two-dimensional heat-conduction equation with erosion or sedimenta-
tion (Eq. (7.19)) has been solved numerically by finite-difference methods.
Three models are illustrated: a model of burial metamorphism, a model of
intrusion and a model of overthrusting. These have been chosen to demonstrate
avariety of possible metamorphic environments and by no means represent the
possible range existing in the Earth. No metamorphic rock is exposed at the
surface without erosion or tectonic accident; but, initially, we discuss hypothetical
cases with no erosion or sedimentation.

7.8.2 Two-dimensional conductive models

Burial metamorphism
A model of a typical burial terrain consists of a granitic country rock in which
a rectangular trough of sediment has been deposited. Beneath both granite and
sediment is a gneissic continental crust overlying the mantle (Fig. 7.18(a)). The
initial temperature gradient in the country rock is the equilibrium gradient. Ini-
tially, we arbitrarily assume the sediment to be at 100 ◦ C throughout and to have
radioactive heat generation of 0.84 Wm − 3 .Amodel such as this could be sim-

ilar to a sedimentary trough formed on a continent above a subduction zone or
to an Archaean greenstone belt filled with thick sediment and set in a granitic
terrain. Figure 7.18(b) shows how the model evolves after 20 Ma. The sediment